Question

Can someone please help walk me through this? Any help is appreciated, thank you!

The graph of f (in blue) is translated a whole number of units horizontally and vertically to obtain the graph g (in red).

The function f is defined by f(x)=|x|.

Write down the expression for g (x).

Answer 1

Explanation:

recall for any function f(x)

Vertical translations by "a" units are given simply by

f(x) + a,

where positive values of a translates the graph in the positive y direction (i.e up) and negative values of a translates the graph in the negative y direction (i.e down)

Horizontal translations by "b" units are given by

f(x-b),

where negative values of a translates the graph in the negative x direction (i.e left) and postive values of a translates the graph in the postive x direction (i.e right)

if we combine the two above, we get the expression

g(x) = f(x-b) + a

In our case, we see that to get from the blue graph to the red graph, we need to translate 3 units in the positive x-direction (i.e b = 3) and 4 units in the negative y-direction (i.e a = -4)

Substituting b = 3, a = -4 and that f(x) = |x|,

we get

g(x) = |x-(3)| - 4

g(x) = |(x-3)| - 4